**Word Problems to Find Area of Quadrilaterals with Vertices :**

Here we are going to see, some practice word problems to find the area of quadrilateral using given vertices.

To find the area of the quadrilateral with the given four vertices, we may use the formula given below.

**Question 1 :**

Let P(11,7) , Q(13.5, 4) and R(9.5, 4) be the mid- points of the sides AB, BC and AC respectively of triangle ABC . Find the coordinates of the vertices A, B and C. Hence find the area of triangle ABC and compare this with area of triangle PQR

**Solution :**

To find the vertices of the triangle from the midpoint of the sides, please visit the page "https://www.onlinemath4all.com/how-to-find-the-vertices-of-a-triangle-if-the-midpoints-are-given.html"

Vertex A :

= (11 + 9.5 - 13.5, 7 + 4 - 4)

= A (7, 7)

Vertex B :

= (11 + 13.5 - 9.5, 7 + 4 - 4)

= B (15, 7)

Vertex C :

= (13.5 + 9.5 - 11, 4 + 4 - 7)

= C (12, 1)

**Area of triangle ABC :**

= (1/2)[(49 + 15 + 84) - (105 + 84 + 7)]

= (1/2)[148 - 196]

= 48/2

Area of triangle ABC = 24 square units

**Area of triangle PQR :**

**P(11,7) , Q(13.5, 4) and R(9.5, 4) **

= (1/2)[(44 + 54 + 66.5) - (94.5 + 38 + 44)]

= (1/2)[164.5 - 176.5]

= (1/2) (12)

Area of triangle PQR = 6

Area of triangle ABC = 4 (Area of triangle PQR)

Let us look into the next example on "Word Problems to Find Area of Quadrilaterals with Vertices".

**Question 2 :**

In the figure, the quadrilateral swimming pool shown is surrounded by concrete patio. Find the area of the patio.

**Solution :**

To find the area of patio, we have to subtract area of EFGH from area of ABCD.

**Area of ABCD :**

= (1/2)[(16 + 80 + 36 + 80) - (-64 - 24 - 100 - 24)]

= (1/2)[(212)-(-212)]

= (1/2)[212+212]

= 212 square units

**Area of EFGH :**

= (1/2)[(6 + 42 + 12 + 30) - (-30 - 6 - 42 - 12)]

= (1/2)[(90)-(-90)]

= (1/2)[90+90]

Area of EFGH = 90 square units

Area of patio = 212 - 90

= 122 square units.

**Question 3 :**

A triangular shaped glass with vertices at A(-5,-4) , B(1,6) and C(7,-4) has to be painted. If one bucket of paint covers 6 square feets, how many buckets of paint will be required to paint the whole glass, if only one coat of paint is applied.

**Solution :**

Area of triangle ABC =

= (1/2)[(-30 - 4 - 28) - (-4 + 42 + 20)]

= (1/2)[-62 - (58)]

= (1/2)[-62 - 58]

= (1/2)(120)

= 60 square feet

Area covered by one bucket of paint = 6 square feets

Required number of bucket = 60 / 6

= 10 buckets

**Question 4 :**

In the figure, find the area of (i) triangle AGF (ii) triangle FED (iii) quadrilateral BCEG

**Solution :**

(i) triangle AGF

= (1/2) [(-2.5 - 13.5 - 6) - (-13.5 - 1 - 15)]

= (1/2) [(-22) - (-29.5)]

= (1/2) (-22+29.5)

= (1/2)[7.5]

= 3.75 square units.

(ii) triangle FED

F (-2, 3) E (1.5, 1) and D (1, 3)

= (1/2)[(-2 + 4.5 + 3) - (4.5 + 1 - 6)]

= (1/2)[(5.5) - (-0.5)]

= (1/2)6

Area of triangle FED = 3 square units.

(iii) B (-4, -2) C (2, -1) E (1.5, 1) G (-4.5, 0.5)

= (1/2)[(4 + 2 + 0.75 + 9) - (-4 - 1.5 - 4.5 - 2)]

= (1/2)[(15.75) - (-12)]

= (1/2)(15.75 + 12)

= (1/2)(27.75)

= 13.875 square units.

After having gone through the stuff given above, we hope that the students would have understood, "Word Problems to Find Area of Quadrilaterals with Vertices".

Apart from the stuff given in this section "Word Problems to Find Area of Quadrilaterals with Vertices", if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**